arXiv subjects

I. G. Pirozhenko

Publications and source records attributed to I. G. Pirozhenko.

At least 19 recordsLinked to original sources

arXiv2025

Casimir effect for scalar field rotating on a disk

We compute the vacuum energy of a scalar field rotating with angular velocity $Ω$ on a disk of radius $R$ and with Dirichlet boundary conditions. The rotation is introduced by a metric obtained by a Galilean transformation from a rest frame. The constraint $ΩR<c$ must be obeyed to maintain causality. To compute the vacuum energy, we use an imaginary frequency representation and the well-known uniform asymptotic expansion of the Bessel function. We use the zeta-functional regularization and separate the divergent contributions, which we discuss in terms of the heat kernel coefficients. The divergences are found to be independent of rotation. The renormalized finite part of the vacuum energy is negative and becomes more negative for larger rotation frequencies.

hep-th↗

arXiv2025

Casimir effect with an unstable mode

We consider the Casimir effect in a (1+1)-dimensional model with a critical mode. Such a mode gives rise to a condensate described by the nonlinear Gross-Pitaevskii equation. In the condensate, there are two sources of the Casimir force; one is the conventional one resulting from the fluctuations, the other follows from the condensate. We consider three simple models that allow for condensate solutions in terms of elliptic Jacobi functions. We also investigate a method for obtaining approximate solutions and show its range of applicability. In all three examples we compute the condensate energy. In one example with a finite interval with Robin boundary conditions on one side and Dirichlet conditions on the other side, we calculate the vacuum energy and the Casimir force. There is a competition between the forces from the condensate and the fluctuations. We mention that the force from the condensate is always repulsive.

quant-ph↗

arXiv2024

Perturbations of classical fields by gravitational shockwaves

Gravitational shockwaves are geometries where components of the transverse curvature have abrupt behaviour across null hypersurfaces, which are fronts of the waves. We develop a general approach to describe classical field theories on such geometries in a linearized approximation, by using free scalar fields as a model. Perturbations caused by shockwaves exist above the wave front and are solutions to a characteristic Cauchy problem with initial data on the wave front determined by a supertranslation of ingoing fields. A special attention is paid to perturbations of fields of pointlike sources generated by plane-fronted gravitational shockwaves. One has three effects: conversion of non-stationary perturbations into an outgoing radiation, a spherical scalar shockwave which appears when the gravitational wave hits the source, and a plane scalar shockwave accompanying the initial gravitational wave. Our analysis is applicable to gravitational shockwaves of a general class including geometries sourced by null particles and null branes.

gr-qc↗

arXiv2024

Gravitational Waves Generated by Null Cosmic Strings

Null cosmic strings are shown to disturb gravitational fields of massive bodies and create outgoing gravitational waves (GW). Perturbations of the metric caused by a straight null string and a point-like massive source are found as solutions to linearized Einstein equations on a flat space-time. An analytic approximation for their asymptotic at future null infinity is derived. A space-time created by the source and the string is shown to have asymptotically polyhomogeneous form. We calculate GW flux in such space-times and demonstrate that the averaged intensity of the radiation is maximal in the direction of the string motion. Opportunities to detect null string generated gravity waves are briefly discussed.

gr-qc↗

arXiv2023

Electromagnetic Waves Generated by Null Cosmic Strings Passing Pulsars

Null cosmic strings disturb electromagnetic (EM) fields of charged sources and sources with magnetic moments. As has been recently shown by the authors, these perturbations result in a self-force acting on the sources and create EM waves outgoing from the sources. We develop an analytic approximation for asymptotic of the EM waves at the future null infinity and calculate radiation fluxes for sources of the both types. For magnetic-dipole-like sources the radiation flux depends on orientation of the magnetic moment with respect to the string. Estimates show that the peak power of the radiation can be quite large for null strings moving near pulsars and considerably large in case of magnetars. The string generated variations of the luminosities of the stars can be used as a potential experimental signature of null cosmic strings.

gr-qc↗

arXiv2022

Electrodynamics under Action of Null Cosmic Strings

A method to study electromagnetic (EM) effects generated by a straight null cosmic string moving in classical EM fields is suggested. The string is shown to induce an additional EM field which can be described as a solution to homogeneous Maxwell equations with initial data set on a null surface, the string event horizon, where the string world-sheet belongs to. The initial data ensure the required holonomy of the string space-time caused by the gravity of the string. This characteristic initial value problem is used to study interaction of plane waves with null strings and perturbations by the strings of the Coulomb fields of electric charges. It is shown that parts of an incoming EM wave crossing the string horizon from different sides of the string are refracted with respect to each other and leave behind the string a wedge-like region of interference. A null string moving near an electric charge results in two effects: it creates a self-force of the charge and induces a pulse of EM radiation traveling away from the charge in the direction close to trajectory of the string.

gr-qc↗

arXiv2020

The closed piecewise uniform string revisited

We reconsider the composite string model introduced {30 years ago} to study the vacuum energy. The model consists of a scalar field, describing the transversal vibrations of a string consisting of piecewise constant sections with different tensions and mass densities, keeping the speed of light constant across the junctions. We consider the spectrum using transfer matrices and Chebyshev polynomials to get a closed formula for the eigenfrequencies. We calculate vacuum and free energy as well as the entropy of this system in two approaches, one using contour integration and another one using a Hurwitz zeta function. The latter results in a representation in terms of finite sums over polynomials. Several limiting cases are considered as well, for instance, the high-temperature expansion, which is expressed in terms of the heat kernel coefficients. The vacuum energy has no ultraviolet divergences, and the corresponding heat kernel coefficient $a_1$ is zero due to the constancy of the speed of light. This is in parallel to a similar situation in macroscopic electrodynamics with isorefractive boundary conditions.

hep-th↗

arXiv2017

Casimir effect for Dirac lattices

We consider polarizable sheets, which recently received some attention, especially in context of the dispersion interaction of thin sheets like graphene. These sheets are modeled by a collection of delta function potentials and resemble "zero range potentials", known in quantum mechanics. We develop a theoretical description and apply the so-called "TGTG"-formula to calculate the interaction of two such lattices. Thereby we make use of the formulation of the scattering of waves off such sheets provided earlier. We consider all limiting cases, providing link to earlier results. Also, we discuss the relation to the pairwise summation method.

quant-ph↗

arXiv2015

Surface plasmons for doped graphene

Within the Dirac model for the electronic excitations of graphene, we calculate the full polarization tensor with finite mass and chemical potential. It has, besides the (00)-component, a second form factor, which must be accounted for. We obtain explicit formulas for both form factors and for the reflection coefficients. Using these, we discuss the regions in the momentum-frequency plane where plasmons may exist and give numeric solutions for the plasmon dispersion relations. It turns out that plasmons exist for both, TE and TM polarizations over the whole range of the ratio of mass to chemical potential, except for zero chemical potential, where only a TE plasmon exists.

cond-mat.mes-hall↗

arXiv2013

Lifshitz formula by spectral summation method

The Lifshitz formula is derived by making use of the spectral summation method which is a mathematically rigorous simultaneous application of both the mode-by-mode summation technique and scattering formalism. The contributions to the Casimir energy of electromagnetic excitations of different types (surface modes, waveguide modes, and photonic modes) are clearly retraced. A correct transition to imaginary frequencies is accomplished with allowance for all the peculiarities of the frequency equations and pertinent scattering data in the complex $ω$ plane, including, in particular, the cuts connecting the branch points and complex roots of the frequency equations (quasi-normal modes). The principal novelty of our approach is a special choice of appropriate passes in the contour integrals, which are used for transition to imaginary frequencies. As a result, the long standing problem of cuts in the complex $ω$ plane is solved completely. Inconsistencies of some previous derivations of the Lifshitz formula are traced briefly. For completeness of the presentation, the necessary mathematical facts are also stated, namely, solution of the Maxwell equations for configurations under consideration, scattering formalism for parallel plane interfaces, determination of the frequency equation roots, and others.

quant-ph↗

arXiv2011

Vacuum energy in conical space with additional boundary conditions

Total vacuum energy of some quantized fields in conical space with additional boundary conditions is calculated. These conditions are imposed on a cylindrical surface which is coaxial with the symmetry axis of conical space. The explicit form of the matching conditions depends on the field under consideration. In the case of electromagnetic field, the perfectly conducting boundary conditions or isorefractive matching conditions are imposed on the cylindrical surface. For a massless scalar field, the semi-transparent conditions ($δ$-potential) on the cylindrical shell are investigated. As a result, the total Casimir energy of electromagnetic field and scalar field, per a unit length along the symmetry axis, proves to be finite unlike the case of an infinitely thin cosmic string. In these studies the spectral zeta functions are widely used. It is shown briefly how to apply this technique for obtaining the asymptotics of the relevant thermodynamical functions in the high temperature limit.

hep-th↗

arXiv2010

On the Casimir entropy for a ball in front of a plane

The violation of the third law of thermodynamics for metals described by the Drude model and for dielectrics with finite \DC conductivity is one of the most interesting problems in the field of the Casimir effect. It manifests itself as a non-vanishing of the entropy for vanishing temperature. We review the relevant calculations for plane surfaces and calculate the corresponding contributions for a ball in front of a plane. In this geometry, these appear in much the same way as for parallel planes. We conclude that the violation of the 3rd law is not related to the infinite size of the planes.

quant-ph↗

arXiv2008

The Casimir force between dissimilar mirrors and the role of the surface plasmons

We investigate the Casimir force between two dissimilar plane mirrors the material properties of which are described by Drude or Lorentz models. We calculate analytically the short and long distance asymptote of the force and relate its behavior to the influence of interacting surface plasmons. In particular we discuss conditions under which Casimir repulsion could be achieved.

quant-ph↗

arXiv2008

Influence of slab thickness on the Casimir force

We calculate the Casimir force between slabs of finite thickness made of intrinsic and doped silicon with different concentration of carriers and compare the results to those obtained for gold slabs. We use the Drude and the plasma models to describe the dielectric function for the carriers in doped Si. We discuss the possibility of experimentally testing the appropriateness of these models. We also investigate the influence of finite thickness on $VO_2$, which has recently been proposed for Casimir effect measurements testing the metal-insulator transition.

quant-ph↗

arXiv2008

Casimir repulsion and metamaterials

We analyze the conditions for getting the Casimir repulsion between two nonequal plates. The force between plates with magnetic permeability defined by Drude or Lorentz models is calculated. The short and long distance limits of the force are derived. The Casimir set-up with the hypothetical perfect matching metamaterial is discussed. We put into question the possibility of getting repulsion within the design of metamaterials based on metallic inclusions.

quant-ph↗

arXiv2007

Spectral Zeta Functions for a Cylinder and a Circle

Spectral zeta functions $ζ(s)$ for the massless scalar fields obeying the Dirichlet and Neumann boundary conditions on a surface of an infinite cylinder are constructed. These functions are defined explicitly in a finite domain of the complex plane s containing the closed interval of real axis $-1\le$ Re $s \le 0$. Proceeding from this the spectral zeta functions for the boundary conditions given on a circle (boundary value problem on a plane) are obtained without any additional calculations. The Casimir energy for the relevant field configurations is deduced.

hep-th↗

arXiv2005

Spectral analysis of a flat plasma sheet model

The spectral analysis of the electromagnetic field on the background of a infinitely thin flat plasma layer is carried out. This model is loosely imitating a single base plane from graphite and it is of interest for theoretical studies of fullerenes. The model is naturally split into the TE-sector and TM-sector. Both the sectors have positive continuous spectra, but the TM-modes have in addition a bound state, namely, the surface plasmon. This analysis relies on the consideration of the scattering problem in the TE- and TM-sectors. The spectral zeta function and integrated heat kernel are constructed for different branches of the spectrum in an explicit form. As a preliminary, the rigorous procedure of integration over the continuous spectra is formulated by introducing the spectral densityin terms of the scattering phase shifts. The asymptotic expansion of the integrated heat kernel at small values of the evolution parameter is derived. By making use of the technique of integral equations, developed earlier by the same authors, the local heat kernel (Green's function or fundamental solution) is constructed also. As a by-product, a new method is demonstrated for deriving the fundamental solution to the heat conduction equation (or to the Schrödinger equation) on an infinite line with the $δ$-like source. In particular, for the heat conduction equation on an infinite line with the $δ$-source a nontrivial counterpart is found, namely, a spectral problem with point interaction, that possesses the same integrated heat kernel while the local heat kernels (fundamental solutions) in these spectral problems are different.

hep-th↗

arXiv2005

Integral Equations for Heat Kernel in Compound Media

By making use of the potentials of the heat conduction equation the integral equations are derived which determine the heat kernel for the Laplace operator $-a^2Δ$ in the case of compound media. In each of the media the parameter $a^2$ acquires a certain constant value. At the interface of the media the conditions are imposed which demand the continuity of the `temperature' and the `heat flows'. The integration in the equations is spread out only over the interface of the media. As a result the dimension of the initial problem is reduced by 1. The perturbation series for the integral equations derived are nothing else as the multiple scattering expansions for the relevant heat kernels. Thus a rigorous derivation of these expansions is given. In the one dimensional case the integral equations at hand are solved explicitly (Abel equations) and the exact expressions for the regarding heat kernels are obtained for diverse matching conditions. Derivation of the asymptotic expansion of the integrated heat kernel for a compound media is considered by making use of the perturbation series for the integral equations obtained. The method proposed is also applicable to the configurations when the same medium is divided, by a smooth compact surface, into internal and external regions, or when only the region inside (or outside) this surface is considered with appropriate boundary conditions.

hep-th↗